BOSTON (CBS) — It’s difficult for any undrafted player to earn a guaranteed contract on an NBA roster. You’ve got hundreds of players competing for few open roster spots at the end of benches around the league.

Chris Johnson had been one of those guys competing for those spots for the last couple of years. That is, until now. The Celtics are expected to sign the swingman for the remainder of the season today, an extraordinary feat given the long odds Johnson had to overcome.

After graduating from Dayton in 2012, Johnson went through the disappointment of not being picked during the 2012 NBA Draft. Instead of chasing money overseas, Johnson played in the D-League last year, where he got a whiff of the NBA on two 10-day contracts with the Memphis Grizzlies.

Two is the maximum number of 10-day contracts a player can sign with a team, after which the team must make a decision on whether it wants to sign the player for the rest of the year. Last year, the Grizzlies ultimately elected not to sign Johnson after his deals expired. No other team gave Johnson another shot as well, as he finished his rookie year in the D-League.

To start this season, the road for Johnson or any other young player to earn a guaranteed roster spot on the Celtics was particularly daunting. The Celtics entered the season dangerously close to the $71.7 million luxury tax threshold, a number the team is determined to stay under in the midst of rebuilding this season.

The Celtics made a couple of trades last month to get a little more breathing room below that tax threshold, but with the trade deadline approaching, there’s no doubt Danny Ainge still wants salary flexibility. He didn’t want or need another guaranteed contract on his roster … unless the player blew him and Brad Stevens away.

Enter the 23-year-old Johnson. Signed with little fanfare to a 10-day contract on Jan. 17, expectations were understandably low out of the gate. The Celtics needed depth after a number of injuries and trades, and they also needed to replace the 3-point shooting of Jordan Crawford and Courtney Lee.

In his first game action, Johnson scored 11 points in a close loss to the Miami Heat. He posted double-digit scoring outputs in the three of his first five games with Boston, while also playing well on the defensive end of the floor.

After being signed to a second 10-day contract two weeks ago, Johnson has remained a permanent fixture in Stevens’ rotation, while shooting a team-best (for guards) 40 percent from 3-point range. Stevens spoke on Johnson’s impact on the floor during his stint thus far.

“I think it’s more motor than speed,” Stevens explained. “If you lined everybody up and ran them in a contest running up and down the court, I don’t know that he’d win, necessarily, against everybody in the NBA. But I think his desire to get there every time, his conditioning level’s excellent, and he’s been well-drilled prior to getting here with those things as well. You see that all the time. We talk about big guys with motors a lot. You don’t always talk about that with guards and wings. He’s got a high motor. He gets to his spots quickly.”

Decision day came yesterday with his final 10-day contract set to expire at midnight. Had he done enough to impress the front office to overlook the potential tax threshold concerns and earn the guaranteed contract he had long sought? The answer was a surprising yes, as the team told him before practice Thursday that it planned to sign him for the rest of the season.

“I just have to give thanks to Danny Ainge,” Johnson said after hearing the news, “for bringing me in and giving me the opportunity, and Brad Stevens for giving me the opportunity to play when guys were injured. And my teammates for just giving me confidence.”

Upon hearing his contract, Johnson did what any good son would do — call his family.

“I called my mom, just to let her know about the news, and she was pretty excited, too,” Johnson said.

While it’s a true underdog story for the undrafted second-year guard to make the cut with this year’s team, Stevens voiced yesterday his confidence that Johnson belonged in the league.

“To me, the greatest stories in sports start with a chip on your shoulder,” said Stevens. “Johnson had got an automatic chip. Now the key is, as you get extended opportunities, is to keep the chip. To keep hungry. That’s another human-nature test. That’s the next one coming for guys like that. I think it’s a great story, but it’s not like it’s some miracle.”

Now it’s up to Johnson to turn his chance over the remainder of the year into a full-time gig. With the potential for a roster shakeup in the next few weeks, one thing is clear: Johnson will continue to get an opportunity.

Brian Robb covers the Celtics for CBS Boston and contributes to NBA.com, among other media outlets. You can follow him on Twitter @CelticsHub.